Problem: Solve for $x$ : $x^2 - 5x + 4 = 0$
Answer: The coefficient on the $x$ term is $-5$ and the constant term is $4$ , so we need to find two numbers that add up to $-5$ and multiply to $4$ The two numbers $-4$ and $-1$ satisfy both conditions: $ {-4} + {-1} = {-5} $ $ {-4} \times {-1} = {4} $ $(x {-4}) (x {-1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -4) (x -1) = 0$ $x - 4 = 0$ or $x - 1 = 0$ Thus, $x = 4$ and $x = 1$ are the solutions.